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Quantum Fingerprinting: Difference between revisions
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** The client now sends this fingerprint to the server through a quantum channel. Both the clients do this process simultaneously. | ** The client now sends this fingerprint to the server through a quantum channel. Both the clients do this process simultaneously. | ||
* '''Server's test''': The server receives the two fingerprints from both the clients and performs the [[Glossary#SWAP test|quantum SWAP Test]] on these states to check if the states are distinguishable. The server independently repeats this SWAP test on fingerprints several times to reduce the error probability in detecting if the two states are different. | * '''Server's test''': The server receives the two fingerprints from both the clients and performs the [[Glossary#Quantum SWAP test|quantum SWAP Test]] on these states to check if the states are distinguishable. The server independently repeats this SWAP test on fingerprints several times to reduce the error probability in detecting if the two states are different. | ||
==Hardware Requirements== | ==Hardware Requirements== | ||
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* <math>c</math>: Parameter for error correcting code. <math>m=cn, c>1</math> | * <math>c</math>: Parameter for error correcting code. <math>m=cn, c>1</math> | ||
* <math>\delta</math>: Parameter for error correcting code. <math>\delta<1</math>. | * <math>\delta</math>: Parameter for error correcting code. <math>\delta<1</math>. | ||
* <math>\epsilon</math>: Error probability | |||
* <math>k</math>: Number of times a fingerprint is repeated, <math>k \in O(log{}{\frac{1}{\epsilon}})</math> | |||
==Properties== | ==Properties== | ||
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'''Output''': <math>|h_x\rangle</math>, <math>|h_y\rangle</math> sent to server </br> | '''Output''': <math>|h_x\rangle</math>, <math>|h_y\rangle</math> sent to server </br> | ||
'''Stage 1''': Client's preparation | '''Stage 1''': Client's preparation | ||
* First client prepares | * First client prepares <math>|h_x\rangle</math> from <math>x</math>, <math>|h_x\rangle = \frac{1}{\sqrt{m}}\sum_{i=1}^{m} |i\rangle|E_i(x)\rangle</math> | ||
* Second client prepares | * Second client prepares <math>|h_y\rangle</math> from <math>y</math>, <math>|h_y\rangle = \frac{1}{\sqrt{m}}\sum_{i=1}^{m} |i\rangle|E_i(y)\rangle</math> | ||
* Both clients send <math>|h_x\rangle</math>, <math>|h_y\rangle</math> to | * Both clients send <math>|h_x\rangle</math>, <math>|h_y\rangle</math> to server | ||
'''Stage 2''': Server's test | '''Stage 2''': Server's test | ||
* Server prepares an ancilla qubit <math>|0\rangle</math> for | * Server prepares an ancilla qubit <math>|0\rangle</math> for SWAP test and starts with state <math>|0\rangle|h_x\rangle|h_y\rangle</math> | ||
* Server | * Server applies gate <math>G = {(H\otimes I)(c-SWAP)(H\otimes I)}</math>, resulting in final state <math>\frac{1}{2}|0\rangle(|h_x\rangle|h_y\rangle + |h_y\rangle|h_x\rangle) + \frac{1}{2}|1\rangle(|h_x\rangle|h_y\rangle - |h_y\rangle|h_x\rangle)</math> | ||
* The server measures the first qubit and transmits the | * The server measures the first qubit and transmits the result to both the clients. | ||
==Further Information== | ==Further Information== | ||
* To reduce the error probability to any <math>\epsilon</math>, the fingerprint of <math>x</math> should be set to <math>|h_x\rangle^{\otimes k}</math>, for a suitable <math>k \in O(log{}{\frac{1}{\epsilon}})</math> | |||
==Related Papers== | ==Related Papers== | ||
<div style='text-align: right;'>''*contributed by Rhea Parekh''</div> | <div style='text-align: right;'>''*contributed by Rhea Parekh''</div> | ||